The present invention relates generally to diagnostic imaging and, more particularly, to a system and method of calculating linear combination coefficient weights used for reconstructing magnetic resonance (MR) images in a parallel acquisition scan.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, or “longitudinal magnetization”, MZ, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated and this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
One technique that has been developed to accelerate MR data acquisition is commonly referred to as “parallel imaging” or “partial parallel imaging”. In parallel imaging, multiple receiver coils acquire data from a region or volume of interest. Thus, parallel imaging is used to accelerate data acquisition in one or more dimensions by exploiting the spatial dependence of phased array coil sensitivity. Parallel imaging has been shown to be not only successful in reducing scan time, but also in reducing image blurring and geometric distortions. Moreover, parallel imaging can be used to improve spatial or temporal resolution as well as increased volumetric coverage.
There are several types of parallel imaging reconstruction methods that have been developed to generate the final, unaliased image from accelerated data. One such group of methods is auto-calibrating based techniques, which calculate reconstruction weights (i.e., linear combination coefficient weights) necessary to synthesize unacquired data directly from acquired data in k-space using an algorithm that does not require coil sensitivity estimates. In such auto-calibration based techniques, the reconstruction weights are calculated from a small amount of fully sampled calibration data that is typically embedded within the scan (i.e., “self-calibration”), but can also be acquired before or after the scan.
As an example, in the GRAPPA method, the linear combination weights are determined directly from the fully sampled calibration data. That is, a set of linear combination weights is generated by way of one or more systems of linear equations. Calibration data is entered into a matrix in the linear equations to determine the linear combination weights. While the filling of such matrices with the calibration data allows for accurate calculation of the linear combination weights, the large amount of data increases the size of the matrices, which leads to a computation time that is greater than what is desirable. For example, a matrix of 100×5000 (2-D) or 300×50,000 (3-D) is not uncommon in many GRAPPA based techniques. A matrix size of that magnitude can be problematic for 2D reconstructions. Furthermore, the size of the matrices increases exponentially with the reconstruction of 3-D images as compared to 2-D images, leading to an even greater length of computation time for 3-D image reconstruction.
It would therefore be desirable to have a method for calculating the linear combination coefficient weights used in many parallel imaging methods that reduces the computation time necessary for image reconstruction. It would also be desirable for such a method to achieve and maintain high image quality results in the reconstruction and for the method to be applicable to a number of different parallel imaging techniques.